The Modeling and Simulation of Tight Gas Reservoirs Incorporating Desorption Phenomena

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The Modeling and Simulation of TightGas Reservoirs Incorporating DesorptionPhenomenaM. A. Ekramzadeh a , S. Gerami b , R. Arabjamaloei c & E. Jamshidi de

a Petroleum Engineering Department , University of Calgary ,Calgary , Alberta , Canadab National Iranian Oil Company , Tehran , Iranc Department of Petroleum Engineering , Islamic Azad University,Omidiyeh Branch , Omidiyeh , Khuzestan , Irand Curtin University of Technology , Bentley , Australiae Petroleum University of Technology , Tehran , IranPublished online: 20 Aug 2012.

To cite this article: M. A. Ekramzadeh , S. Gerami , R. Arabjamaloei & E. Jamshidi (2012) TheModeling and Simulation of Tight Gas Reservoirs Incorporating Desorption Phenomena, EnergySources, Part A: Recovery, Utilization, and Environmental Effects, 34:20, 1855-1867, DOI:10.1080/15567031003753561

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Energy Sources, Part A, 34:1855–1867, 2012

Copyright © Taylor & Francis Group, LLC

ISSN: 1556-7036 print/1556-7230 online

DOI: 10.1080/15567031003753561

The Modeling and Simulation of Tight Gas

Reservoirs Incorporating Desorption Phenomena

M. A. EKRAMZADEH,1 S. GERAMI,2 R. ARABJAMALOEI,3

and E. JAMSHIDI4;5

1Petroleum Engineering Department, University of Calgary, Calgary, Alberta,

Canada2National Iranian Oil Company, Tehran, Iran3Department of Petroleum Engineering, Islamic Azad University, Omidiyeh

Branch, Omidiyeh, Khuzestan, Iran4Curtin University of Technology, Bentley, Australia5Petroleum University of Technology, Tehran, Iran

Abstract Tight gas reservoirs are categorized as unconventional gas reservoirs. One

of the main characteristics of a tight gas reservoir is the adsorption of gas on therock surface due to high specific surface area. Desorption is the process of adsorbing

gas by the reservoir rock on its surface that is dependent on factors, such as reservoir

pressure, reservoir rock type, and temperature. Therefore, analysis of production datausing conventional methods is expected to be problematic. In this study, there was

an endeavor to model and simulate the desorption phenomena in tight formationsto investigate its effect on different properties and to study related reservoirs. The

purpose of this work is to model the single-phase radial gas flow in tight gas reservoirsincluding equilibrium desorption phenomena on the rock surface and Darcy flow in

a reservoir. Considering a control volume, the gas desorption rate as a function oftime and space is incorporated into the radial continuity equation as a source term.

Using a Langmuir-type sorption isotherm, the gas desorption rate is determined atany radius of the reservoir. The resulting governing equation is solved numerically

using a finite difference approach. The simulator is used to model a tight reservoirto identify how important parameters affect the performance of a tight gas reservoir.

The results suggest that the development of tight gas reservoirs with significant gasdesorption can lead to higher production rates and improve the productivity of the gas

reservoir. The model developed here can be used as an engineering tool for evaluatingthe role of adsorbed gases in improving the productivity and extending the life of tight

gas reservoirs.

Keywords desorption phenomenon, gas-rock interaction, numerical simulation, reser-voir modeling, tight gas reservoir

1. Introduction

The increased demand for new gas reserves validate the need for an accurate estimate of

the reservoirs characteristics, such as gas in place estimation in the early life of a well

that leads to evaluating the offset development or infill drilling, well spacing, and design

of wellhead facilities.

Address correspondence to Mohammad Ekramzadeh, Petroleum Engineering Department,University of Calgary, Calgary, Canada. E-mail: [email protected]

1855

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1856 M. Ekramzadeh et al.

What makes a significant difference between the production mechanisms of tight gas

reservoirs and conventional reservoirs is the intrinsic behavior of tight reservoirs for their

very low permeability. Most gas reservoirs deliver needed data for primary evaluation

within 24 to 72 h, depending on the reservoir characteristics. But this time cannot be kept

up with, since this time is so little for a tight formation to produce as much to extract

the inquired data.

All of the above features stimulate people to derive new methods of production

processes for tight gas formations. Bennett and Forgerson (1975) made an effort to

make new ways for reserve prediction using limited performance data. Gochnour and

Slater (1977) established ways for well test analysis of tight gas formations (Bennett and

Forgerson, 1975), while Crafton et al. (1982) described the producing well evaluation in

tight gas reservoirs.

Tight gas reservoirs lack a unique definition. Law and Curtis (mentioned in Gochnour

and Slater, 1977) define the low permeability reservoirs as having permeability less than

0.1 millidarcies (Gochnour and Slater, 1977; Naik).

DGMK, the German Society for Petroleum and Coal Science and Technology,

declared a definition for tight gas reservoirs as reservoirs with the effective permeability

of less than 0.6 millidarcies.

As in the definition of tight gas reservoirs, the matrix medium is poorly enabled to

transmit thefluid through theporespaces.Thiswill be intensified when weknowthat thehuge

amount of gas reserve should be extracted. People decided to make ways for the underlying

fluid, so hydraulic fracturing of tight gas formations appeared as the accepted method

fulfilling this goal. Hydraulically fractured horizontal wells, in particular, are the proven

technology to produce gas from tight formations. Hydraulic fractures reduce well drawdown,

increase productivity of horizontal wells by increasing the surface area in contact with

formation, and provide high conductivity paths to wellbore (Shahamat and Gerami, 2009).

Tight gas reservoirs support an outstanding supply of gas that is derived from un-

conventional gas reservoirs. They are different in the production amount and mechanism

since a large portion of the gas phase in the formation is adsorbed on the surface of the

low permeable matrix with the sorption mechanism, which is controlled by pressure. As

the pressure declines, this adsorbed amount of gas will release gradually in the form of

free gas and starts to flow towards the wellbore. If the reservoir is considered as a naturally

fractured reservoir, this flow will fill the fracture medium and start to move towards the

wellbore using the fracture wideness. Therefore, adsorbed gas has an important role in

long-term production scenarios, while it also causes the production forecasts to be more

realistic (Satik et al., 1995).

The volume of gas adsorbed as a function of pressure is considered as the adsorption

isotherm. Among all the adsorption isotherms, the Langmuir isotherm is the most popular

one, which is described in the following equation (Gao and John Lee, 1994):

VE DVLPg

PL C Pg

; (1)

where PL is the Langmuir pressure at which the total gas volume is adsorbed, VE is

equal to one half of the Langmuir volume, VE is total volume of gas adsorbed per unit

volume of the reservoir in equilibrium at pressure Pg , and VL is the Langmuir volume,

which is the maximum capacity of sorption for the rock type.

There also exists some other types of adsorption isotherms that are included as

Freundlich isotherm and Henry’s law.

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Tight Gas Reservoirs 1857

The Freundlich isotherm is as follows:

Veq D VF P NFg ; (2)

where NF is the integer number of multiple boreholes and VF is the amount of gas

adsorbed per unit volume of the reservoir (Gao and John Lee, 1994).

Henry’s law is also indicating a kind of adsorption isotherm, which is highly depen-

dent on the pressure. It is described as:

Veq D VH Pg ; (3)

where VH is Henry’s law volume constant (Gao and John Lee, 1994).

The Langmuir isotherm is generally used to describe the mono player adsorption be-

cause with increasing pressure, the amount of adsorbed gas asymptotically approaches its

final possible amount of adsorbed gas volume (Fathi and Akkutlu, 2009). Since Freundlich

isotherm assumes no end for the adsorption capacity of the rock reservoir in any pressure,

it is widely used in multi layer reservoirs with adsorption phenomenon (Fathi and Akkutlu,

2009). Both Langmuir and Freundlich isotherms are finally collapsed on Henry’s law.

Fathi and Akkutlu (2009) studied the upscaling approach to investigate the effect

of small scale heterogeneities in matrix porosity on Darcy flow in the existence of

adsorption. The study had some malfunctions which were cured by their next paper

with the consideration of nonlinear sorption kinetics and a transport mechanism for the

adsorbed phase (Fathi and Akkutlu, 2009). Also, the unsteady state nature of sorption

phenomenon was studied with the diffusion actions of the reservoir in 1990 by Kolesar

et al. (Fathi and Akkutlu, 2009; Stotts et al., 2007).

The modeling of unconventional gas recovery was then investigated in 1991 by

King and Ertekin, who tried to compare the mechanism of desorption in coalbed and

tight formations (King and Ertekin, 1991a, 1991b). They also considered several fea-

tures that were distinguished, such as various gas transport mechanisms and allowance

for composite conventional and unconventional formations (Fathi and Akkutlu, 2009).

Langmuir and Freundlich were the desorption isotherms included.

2. Approach

As mentioned in the previous section, desorption process may be treated in two ways:

pseudo steady state and unsteady state mechanism. Dealing with the tight gas reservoirs,

the governing equations should account for the desorption phenomenon. Thus, it will be

seen that the governing equations are derived as nonlinear ones.

Two ways of processing these nonlinear equations exists:

1. Making simplified assumptions to transfer nonlinear equations into linear ones to

solve analytical form;

2. Treating the solution through a numerical approach.

What is expected in this endeavor is to verify whether desorption is influential on the

production of tight formations or not. So, it is clear that the analytical solution may not

be necessary. Then the numerical approach remains.

2.1. Methodology

The methodology is the step-by-step process of solving the nonlinear equation:

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1. Description of the physical model (single well, cylindrical reservoir);

2. Simplifying assumptions;

3. Mathematical model:

a. Mass balance equation;

b. Momentum equation (Darcy’s flow);

c. Equation of State;

d. Initial and Boundary Condition;

4. Numerical Solution;

5. Sensitivity study on important reservoir and rock parameters.

2.2. Physical Model

The reservoir is considered to be a cylindrical reservoir with the external radius of re and

the reservoir thickness of h. The well is also considered to be well located at the center

of the reservoir. There is not any conception of wellbore storage for simplicity.

The reservoir fluid flow is considered to be single phase flow of the gaseous phase.

All the required reservoir characteristics are assumed, in a way, to simplify the problem.

2.3. Mathematical Model

In order to derive the governing equation in the tight gas formations, the physical model

should be transferred into mathematical form to make ways to solve it.

In the first order, the usual gas reservoir is developed that gains no sign of the

adsorption process. The only factor that may change the usual derivation of the gov-

erning equation is the tight gas reservoirs characterization of having low permeability

values. Once the tight formations are evaluated by deriving the governing equation, then

desorption phenomenon should be inserted to account for it. This is the overlooked

procedure of mathematical modeling.

The whole procedure may be summarized as follows:

1. Derivation of continuity equation for gas reservoirs;

2. Accounting for the adsorption equation in the governing the equation;

3. Derivation of the final governing equation;

4. Determining the initial and boundary conditions;

5. Numerical simulation development.

2.4. Continuity Equation

In order to derive the continuity equation, the basis should be designed. It is usual to

start with the linear flow.

Rate of mass in � rate of mass out C net rate of mass generation D rate of mass

accumulation:

�r�u D@

@t.��/ C Oq; (4)

VE DVLPg

PL C Pg

; (5)

�r�u D@

@t.��/ C

@

@t.�gVE/: (6)

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2.5. Initial and Boundary Conditions

The diffusivity equation of tight gas reservoir considering desorption phenomena is a

partial differential equation that is formulated upon two parameters of time and direction,

i.e., time and direction for solving these sorts of partial differential equations, there should

exist some assumptions, such as initial and boundary conditions.

In this investigation, boundary conditions are considered to be a constant rate at the

inner boundary and no flow boundary at the outer boundary. Also, the time boundaries

known in the case of conventional gas reservoirs are treated the same.

2.6. Numerical Simulation

The radial single phase compressible fluid reservoir with desorption is investigated with

the following equations as the final governing equation:

1

r

@

@r

�

rP

z

k

�

@P

@r

�

D@

@t

�

P

z�

�

C@

@t.�gVE /

1

r

@

@r

�

rk

�z

@P 2

@r

�

D

�

�C

zC VL

�

C

z.PL C P /P C

1

z

P

.PL C P /2

��

@P 2

@t;

Di Fi� 1

2

P 2nC1

i�1 � Di

�

Fi� 1

2

C FiC 1

2

C1

Di

�

P 2nC1

i C Di FiC 1

2

P 2nC1

iC1 D �P 2n

i

(7)

where

Fi D

�

1:127

5:615

rk

�z�r

�

i

Di D�t

ri �ri

�

�C

zC VL

�

C

z.PL C P /P C

PL

z.PL C P /2

�� :(8)

2.7. Running the Simulator

Once the simulator is developed, a base case was introduced to test the simulator. It is

important to remind that the aim of this simulator is to investigate the effects of desorption

process in the production and performance of the tight gas reservoirs.

A tight formation with the sequential characteristics is modeled and then simulated

to get the reservoir behavior as follows. The tight formation is considered not to have

any sign of desorption.

Figure 1 is illustrating a tight gas reservoir, which definitely has small characteristic

values of permeabilities of tight formations. The reservoir is considered to be divided

into 1,000 grid blocks with the outer radius of 1,000 ft. Once the desorption term is

inserted, Figure 2 is derived to get the first start of comparing the two conditions with

and without desorption tight formations.

What first appears in the first analysis is a sign of separation between two graphs, in

which the only reason taken into consideration is the desorption action of tight formation.

It is important to note here the point that desorption starts to release the adsorbed gas

from the rock surface while the pressure is declining. Figure 3 shows the two different

behaviors. The investigation shows that desorption seems to be very effective in the early

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Figure 1. Tight gas reservoirs without desorption. (color figure available online)

steps of production. Figure 4 is demonstrating that desorption is helping the pressure not

to decline as much as in the non-adsorptive case. Table 1 contains the base case data for

running the base case scenario.

3. Sensitivity Analysis

3.1. Effect of Langmuir Pressure in the Reservoir Performance

Langmuir pressure is described as the pressure at which the amount of desorbed gas is

equal to one half of the total amount of desorbed gas, VL. As the definition describes, this

Figure 2. Difference of desorption tight gas reservoirs and normal tight gas reservoirs. (color figure

available online)

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Figure 3. Comparisons of tight gas reservoirs with desorption and without desorption. (color figure

available online)

parameter may not have any physical interpretation and is used as the auxiliary factor.

Figure 5 is describing a prototype of change in the Langmuir pressure. The time of

production is assumed to be 1 month. Figure 6 illustrates the same trend in a semilog plot.

The analysis of the effect of Langmuir pressure on the pressure distribution in a

desorption-dominant tight reservoir may be more accurate if the desorption isotherms are

investigated. Figures 7 and 8 are demonstrating the behavior of a Langmuir desorption

isotherm regarding the changes in the Langmuir pressure. It is easily indicated that,

with any increase in the amount of Langmuir pressure, the amount of desorbed gas

Figure 4. Effect of desorption in the early stages of production, after 15 days. (color figure avail-

able online)

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Table 1

Data for the base case

Variable Value

Pi 2,000 psia

T 600 R

Pc 667 psia

Tc 343 F

MW 16 lbm/lbm

' 0.2

k 0.01 md

h 10 ft

q 1,000 SCF/day

PL 174.93 psia

VL 4.48 cm3/g

rw 0.35 ft

re 1,000 ft

is decreased. This may be due to the fact that lower Langmuir pressure leads to the

desorption occurrence earlier than the higher Langmuir pressure, which causes a larger

amount of desorbed gas.

The isotherms plots are illustrating how the amount of desorbed gas is influenced by

the amount of Langmuir pressure; however, these precise and distinct changes may not

be seen as clearly in the pressure profiles. Investigating the trend of the isotherms plot

will reveal that the desorption rate is higher in low pressures compared with the high

pressure, since the slope of the isotherm slope is steeper in pressures around 500 than

that of around 1,500.

Figure 5. Effect of Langmuir pressure. (color figure available online)

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Figure 6. Semilog plot of Langmuir pressure change on the desorption action. (color figure avail-

able online)

3.2. Effect of Langmuir Volume in the Reservoir Performance

Langmuir volume is the maximum capacity of rock to adsorb gas on its surface. Langmuir

volume represents a sort of rock characteristic, hence, the reservoir characteristic. The

sensitivity analysis of Langmuir volume reveals that this factor has great influence on

the reservoir performance and on the amount of gas desorbed as the pressure declines.

Figure 7. Plot of desorption isotherms for different values of Langmuir pressure. (color figure

available online)

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Figure 8. Semi-log plot of desorption isotherms for different values Langmuir pressure. (color

figure available online)

Any small change in Langmuir volume is clear in the small changes of the desorption

results. This trend shows that lowering the Langmuir volume will lead to lower amounts

of desorption. In this way, the pressure distribution will rise in a lower amount regarding

the base case in comparison to the tight gas formation without desorption. In Figure 9

the time of production is assumed to be 1 month.

Figure 9. Effect of change in Langmuir volume. (color figure available online)

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Figure 10. Desorption isotherms for different values of Langmuir volume. (color figure available

online)

As can be seen, there is a complete distinction between the cases of changing in

the Langmuir volume. Figure 10 illustrates the behavior of Langmuir isotherm while the

change in Langmuir volume occurs.

3.3. Effect of Production Flow Rate in the Reservoir Performance

The pressure seems to be increased as the production rate is decreasing. Figure 11

illustrates this role of the change in the production rate. As the production rate increases,

more adsorbed gas will release due to the pressure drop. Although the amount of pressure

drop will be compensated by the desorbed gas, continuous production with a higher rate

leads to a higher pressure drop.

4. Conclusion and Recommendation

Tight gas reservoirs are sources of gas energy in which the actual intrinsic properties and

characteristics may have not been found yet. Desorption is just a production mechanism

in which the overall process of production is not influenced, but sorption phenomena act

as a sort of source term in the derivation of governing equations.

4.1. Conclusion

The project was to develop a model and the regarded simulator in order to investigate the

effect of desorption action in the tight gas reservoirs. Considering this fact, the following

consequences are valid:

1. Desorption cannot be ignored from the behavior of tight gas reservoirs. The

noticeable distinction between desorption-dominated and non-adsorptive tight gas

reservoirs clearly describes the magnificence of the action. The importance of

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Figure 11. Effect of production rate change. (color figure available online)

desorption action may be to show its importance once the reservoir different

characteristics, such as reserve estimation, well testing, history matching, etc.,

are to be evaluated.

2. The sensitivity analysis is performed to investigate the effects of changes in

Langmuir pressure, Langmuir volume, and production rate. Each effect in the

Langmuir properties were considered using the desorption isotherms regarding

the specified characteristics. It was shown that desorption amount will decrease

with the increase in the Langmuir pressure, while the value of Langmuir plays

the reverse behavior. In other words, desorption amount will increase with the

increase in the value of Langmuir volume.

4.2. Recommendation

In this study, there was an endeavor to model and simulate the desorption action of tight

gas reservoirs.

In order to perform this, there were some assumptions to simplify the problem. It

is recommended that whole assumptions are investigated precisely to prevent any source

of error. The recommendations are listed below:

1. Modify the assumptions in order to achieve realistic simulation.

2. Since tight gas reservoirs are mostly treated as naturally fractured reservoirs, it is

highly recommend that the whole process be done considering the tight formation

as double porosity-double permeability reservoir.

3. Insert the terms of diffusion and investigate the proportion of each mechanism in

the production.

4. Investigate the effect of near wellbore hydraulic fracturing in the mechanism and

process of desorption.

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5. Investigate the other desorption isotherms in order to make it clear which isotherm

is suitable enough for the reservoirs of early production time.

6. Perform the whole process for constant pressure conditions in the wellbore bound-

ary.

References

Bennett, E. N., and Forgerson, C. D. 1975. Predicting reserves and forecasting flow rates of

relatively tight gas wells using limited performance data. SPE Paper No. 5058.

Crafton, J. W., Poundstone, D. J., and Brown, C. A. 1982. A practical model for evaluating a

well producing from a tight gas formation. SPE Unconventional Gas Recovery Symposium,

Pittsburgh, PA, May 16–18.

Fathi, E., and Akkutlu, I. Y. 2009. Nonlinear sorption kinetics and surface diffusion effects on gas

transport in low-permeability formations. SPE Paper No. 124478.

Gao, Ch., and John Lee, W. 1994. Modeling multilayer gas reservoirs including sorption effects.

SPE Paper No. 29173.

Gochnour, J. R., and Slater, G. E. 1977. Well test analysis in tight gas reservoirs. SPE Paper No.

6842.

King, G. R., and Ertekin, T. 1991a. State-of-the-art modeling for unconventional gas recovery. SPE

Formation Evaluation, SPE Paper No. 18947.

King, G. R., and Ertekin, T. 1991b. Supplement to SPE 18947: State-of-the-art modeling for

unconventional gas recovery. SPE Formation Evaluation, SPE Paper No. 22285.

Kolesar, J. E., Ertekin, T., and Obut, S. T. 1990. The unsteady state nature of sorption and diffusion

phenomena in the micropore structure of coal: Part 1—Theory and mathematical formulation.

SPE Formation Evaluation.

Naik, G. C. Tight gas reservoirs—An unconventional natural energy source for the future. Available

at: http://www.pinedaleonline.com/socioeconomic/pdfs/tight_gas.pdf

Satik, C., Home, R. N., and Yortsos, Y. C. 1995. A study of adsorption of gases in tight reservoir

rocks. SPE Paper No. 30732.

Shahamat, M. S., and Gerami, Sh. 2009. Tight gas reservoirs: Opportunities, characteristics and

challenges. First International Petroleum Conference & Exhibition, Shiraz, Iran.

Stotts, G. W. J., Anderson, D. M., and Mattar, D. M. 2007. Evaluating and developing tight gas

reservoirs—Best practices. SPE Paper No. 108183.

Nomenclature

C gas compressibility, psi�1

D desorption coefficient

F transmissibility coefficient

k permeability, md

PL Langmuir pressure, psi

Pg reservoir gas pressure, psi

r radius, ft

u reservoir fluid velocity, bblf t2 day

VE desorbed volume,Vdesorbedgas

VReservoir

VL Langmuir volume, ft3/lbm

Z compressibility factor

� gas density, lbm/ft3

' porosity

� viscosity, cp

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The Modeling and Simulation of Tight Gas Reservoirs Incorporating Desorption Phenomena

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